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# Finding Minimum value of an anonymous function using fminbnd

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Emily Davenport on 8 Sep 2020
Commented: Emily Davenport on 8 Sep 2020
Hi,
I am trying to find the minimum value of my anonyus function G, which depends on the variable na. I am getting the error "User supplied obective function mus return a scalar value" when I try to run my code. From some debugging, I can see that if I type G(0) in the command line, I get a 1X1000 double that is just the correct value for G(na=0), but repeated 1000 times. Can anyone help me fix this? Thanks for any advice, I've never posted on here before.
clear all
% Given :
R = 1.987; %[cal/mol*K]
T = 500; %[K]
G0 = -1000; %[cal/mol]
%% Find values to plot G vs. E
% Calulate na for a bunch of E:
% E: [0,1]
E = linspace(0,1,1000); % get 1000 evenly spaced values of E between 0 and 1
na = (.5.*(1-E)); % CHANGE THIS FOR THE EQUATION IN THE PROBLEM
% Calculate G-(ua/2)-(ub/2)
A = (1-(2.*na)); % define this bc it gets used a lot below
G = @(na) ((A.*G0)+((R*T).*((2.*na.*log(na))+(A.*log(A)))));
% plot it
figure();
plot(E, G(na))
title('Free Energy of System, G');
ylabel('G [cal/mol]'); xlabel('E');
% find minimum G value (equilbrium)
[na_min, Gmin] = fminbnd(G,na(end), na(2))

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### Accepted Answer

Bruno Luong on 8 Sep 2020
Edited: Bruno Luong on 8 Sep 2020
You should not mix between discrete sampling of your function G and continuous evaluation required by FMINBND
% Given :
R = 1.987; %[cal/mol*K]
T = 500; %[K]
G0 = -1000; %[cal/mol]
%% Find values to plot G vs. E
% Calulate na for a bunch of E:
% E: [0,1]
E = linspace(0,1,1000); % get 1000 evenly spaced values of E between 0 and 1
na = (.5.*(1-E)); % CHANGE THIS FOR THE EQUATION IN THE PROBLEM
% Calculate G-(ua/2)-(ub/2)
A = @(na) (1-(2.*na)); % define this bc it gets used a lot below
G = @(na) ((A(na).*G0)+((R*T).*((2.*na.*log(na))+(A(na).*log(A(na))))));
% find minimum G value (equilbrium)
[na_min, Gmin] = fminbnd(G,na(end), na(2))
Emin = 1 - na_min/0.5 % recover corresponding energy
figure();
plot(E, G(na),'b',Emin,Gmin,'+r')
title('Free Energy of System, G');
ylabel('G [cal/mol]'); xlabel('E');

#### 1 Comment

Emily Davenport on 8 Sep 2020
Hi Bruno,
Thank you for your help. That makes much more sense now, I had never encoutnered fminbnd before.

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### More Answers (1)

Alan Stevens on 8 Sep 2020
You don't need fminbnd to find the minimum of G. Just
min(G(na))
will do it (or am I missing something?).

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